ARJUN PRAKASH · RESEARCH SYSTEM ONLINE00:00:00 UTC
ONLINEADAPTATION &CONTINUAL LEARNING
VOL. 001 — 2026
01THESIS
The worlddoesn’t holdstill.Learning can’teither.
Learning systems should do more than find a solution once. They should preserve the capacity to adapt as objectives shift, environments change, and other learners respond.
My work studies the dynamics, representations, and interactions that make continued adaptation possible—and the failures that make it disappear.
Spectral Collapse Drives Loss of Plasticity in Deep Continual Learning
Arjun Prakash · Naicheng He · Kaicheng Guo · Saket Tiwari · Ruo Yu Tao · Tyrone Serapio · Amy Greenwald · George Konidaris
IDEA IN MOTION
A neural network can slowly become too rigid to learn anything new. Here, that loss of flexibility appears as a cloud collapsing from many directions into none.
THE PAPER IN BRIEF
Neural networks do not always stay ready to learn. When trained on a stream of new tasks, their internal features can become less flexible until new learning barely works. This paper connects that loss of flexibility to a collapse in the network’s useful directions and explores ways to preserve them for whatever comes next.
CURVATUREDIRECTIONSVANISH
3D SPACE · DIMENSION 34,096 PARTICLES · WEBGL2
DRAG TO ORBIT CLICK TO RESEED
3D FREEDOM→PLANAR MOTION→ONE AXIS→STILLNESS
A deliberately stylized metaphor for dimensionality—not a numerical reconstruction. The same 4,096 particles keep moving, but each collapse removes a direction permanently until the sequence is reset.
03RESEARCH 02 · BILEVEL POLICY OPTIMIZATION
PAPER 02MAY · 2025
ARXIV:2505.11714
REINFORCEMENT LEARNING · BILEVEL OPTIMIZATION
Bi-Level Policy Optimization with Nyström Hypergradients
Arjun Prakash · Naicheng He · Denizalp Goktas · Jacob Makar-Limanov · Amy Greenwald
IDEA IN MOTION
When two parts of a learning system adapt to each other, the order of their updates can determine whether they wander, cycle, or settle.
LIVE SIMULATION
THE PAPER IN BRIEF
An actor decides what to do and a critic judges those decisions. Because both are learning, each update changes the problem faced by the other. This paper treats that relationship as a nested process, allowing the actor to anticipate the critic’s response and move toward more stable solutions.
ACTORHYPERGRADIENTCRITIC
MOVE TO BEND CLICK TO IMPULSE
This is the paper’s toy experiment running live. Each panel starts from the same points, then follows a different learning rule. In the first two, the learners keep circling one another. In the last two, they settle into the same stable outcome. Click anywhere to push the particles apart and watch every rule respond to the same new starting conditions.
04RESEARCH 03 · REACH–AVOID STACKELBERG GAME
PAPER 03NEURIPS · 2023
ARXIV:2401.12437
MULTI-AGENT RL · GAME THEORY
Convex-Concave Zero-Sum Markov Stackelberg Games
Denizalp Goktas · Arjun Prakash · Amy Greenwald
IDEA IN MOTION
Two cars learn through competition: one searches for a route to the goal, while the other learns to intercept it.
THE PAPER IN BRIEF
Many decisions are made against another learner. This paper studies games in which one player commits to a strategy and the other responds, then develops practical ways for both to learn from experience. The reach–avoid experiment turns that idea into a pursuit: reach the target before the opponent can intervene.
REACHBEST RESPONSEDENY
INITIALIZING SELF-PLAYSPARSE REWARD · ALT 4:4 · TWO POLICIES LEARNING LIVE
TOROIDAL WORLD EDGES WRAP · RANDOM SPAWNS
UPDATE SCHEDULE
UPDATE000
SELF-PLAY GAMES0000
REACH WINS · 50 AVG0%
CAPTURES · 50 AVG0%
OUTCOME TIMELINE · ALL SELF-PLAY GAMES · 12-GAME ROLLING RATE
REACH CAPTURE TIMEOUT
Both cars learn from scratch while this tab is open. They receive feedback only when a run ends: the reach car succeeds at the goal and loses if it is captured or runs out of time, while the defender receives the opposite result. Alternating mode lets them take turns learning. Nested mode gives the reach car several attempts to adapt before the defender responds. Each mode keeps its own live history, and the world wraps cleanly at every edge.
05RESEARCH 04 · STRUCTURAL CLUSTERING
PAPER 04AMF · 2022
ARXIV:2004.09963
QUANTITATIVE FINANCE · CHANGE POINTS
Structural Clustering of Volatility Regimes for Dynamic Trading Strategies
Arjun Prakash · Nick James · Max Menzies · Gilad Francis
IDEA IN MOTION
A noisy signal can change character without warning. The detector spots those shifts and colours the stream by how calm or turbulent it has become.
THE PAPER IN BRIEF
Markets do not behave the same way forever. This paper detects moments when their behavior changes, groups similar periods together, and uses those recurring patterns to adjust risk over time—without deciding in advance how many kinds of market there are.
CALMBREAKREGIME
WATCHING FOR CHANGELIVE SIGNAL · CHANGE DETECTION
CALM ACTIVE TURBULENT UNCONFIRMED
DETECTOR SIGNALQUIET
LAST CHANGE—
CONFIRMATION LAG—
REGIMES FOUND01
The line never stops. The detector continually compares recent behaviour with what came before and marks a new regime when that difference becomes convincing. Cyan shows calmer periods, lime shows active periods, and coral shows turbulence. The colours are a visual guide to the intensity of the signal; the paper goes further by grouping similar historical regimes and using them to manage risk.
LIVE TECHNICAL COLOPHON
The research is running on your device.
Nothing here is prerecorded. Each visualization is generated live in your browser from the ideas, dynamics, and experiments behind the papers.
RENDERERDETECTING
COLOR SPACESRGB
FRAME RATE— FPS
MOTIONACTIVE
POINTER X/Y0.00 / 0.00
SCROLL DEPTH000%
END OF THIS TASKREADY FOR THE NEXT
NEVERSTOPLEARNING
Designed and computed at the edge. One page. Live systems. Always adapting.